I'm interested in creating a simple, easy-to-understand way to handle magic for younger players, or for adults entirely new to gaming. For example, if you're meeting people for the first time and running an introductory RPG.

Here goes:

In this simplified system, Magic works like Luck. When you want to cast a spell, roll 2d6. If the result is equal to or lower than your Magic score, the spell goes off as intended; otherwise it doesn't. Either way, reduce your Magic score by one point.

That's it.

Magic points would be regained about as fast as Luck, or maybe fully regained after a night of rest.

I figure this would only work with a very basic spell list, such as found in The Citadel of Chaos, or Legend of Zagor. For example, here's the Amarillian Grimoire from Legend of Zagor:

I like it - since LUCK is your ability for things to work in your favour then it makes sense that people could practise and train to use their luck as a resource to make things work their way when they want.

These spells could scale to make them more powerful if you spend more luck on them. For example, if you spend 1 luck on levitate, it gives a bonus to jump rolls. 2 luck points enable proper levitation up and down and 4 points enable proper flying.

Another way to go is that spending luck points helps, but in ways that makes the character look like they were lucky or that their enemies were unlucky. This limits effects to things such as:

Rerolling dice
Skill bonuses
Skill penalties
Damage reduction
Damage increase
Avoiding fumbles
Finding items you need nearby, even though they are rare
Doing things that are very unlikely to happen, but rely on luck (such as getting 100 straight heads in a row on 100 coin flips or throwing a knife at someone on a spinning target whilst blindfolding and missing them)

Sounds like a fair option for a fairly low magic settings.
If you want to cast more powerful magic you can either increase the LUCK reduction or include ingredients for casting (a bit like Sorcery) or extend the casting time, or, as suggested, apply heavy penalties for miscasting, or... a mix of the above

He's a real Nowhere man, sitting in his Nowhere land, making all his Nowhere plans for Nobody.